\hspace{-16}$Let $\bf{L=\lim_{n\rightarrow \infty}\frac{1}{\frac{1}{\sqrt{2}}.\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}}\big).\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}.............n-terms}\big)}}$\\\\\\ Then $\bf{2\sqrt{3}.\cot(L)=}$
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